Multivariate Statistics for Large Data Sets: Applications to Individual Aerosol Particles

Cluster, discriminant, correlation, and principal component analysis were used for data reduction of the elemental compositions of atmospheric aerosol particles. To verify the methods used, cluster analysis was performed on (1) four clay minerals, (2) U.S.G.S. standard basalt particles, and (3) a complex Phoenix aerosol sample. A generalized scheme was developed for seed-point selection, the determination of the number of clusters, and cluster evaluation. Analysis of variance and testing of cluster significance were used as objective criteria for the evaluation of each step in the scheme. Cluster analysis was effective for determining the types of particles that occurred in the Phoenix aerosol. Discriminant analysis, based on the Phoenix clusters, and analysis of the variance of a multisample data set of aerosol particles from Chandler, a neighboring community to Phoenix, were used to test seed-point selection methods and centrold sets. Correlation and principal component analysis of the Chandler set were used to assess cluster significance and temporal emission patterns. The temporal patterns in Chandler correlated well with upper level wind directions.